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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Testing independence of factor variables in a non-linear specification |

Date |
Mon, 11 Jul 2011 09:18:39 +0200 |

On Sun, Jul 10, 2011 at 9:56 PM, Tanuku AP wrote: > Based on the following snippet, would it be OK to claim that [H0: interaction terms do not matter] null hypothesis cannot be rejected at the 1% and 5% levels? > ***************** > . probit choice age disabled##income i.receduc i.sex, nolog > > . testparm disabled#income > chi2( 4) = 7.89 > Prob > chi2 = 0.0956 > > ************** As usual you must be annoyingly exact when describing a test. The null hypothesis is not "interaction terms do not matter", but "the coefficients for the interaction terms are all 0". The two are not the same, especially in non-linear models like -probit-. If you wish to interpret your coefficients in terms of marginal effects than you can easily end up with very different conclusions, see: Edward C. Norton, Hua Wang, Chunrong Ai (2004), "Computing interaction effects and standard errors in logit and probit models" The Stata Journal, 4(2):154-167. My interpretation of that article (others disagree) is that it illustrates the limits of usefulness of marginal effects. Marginal effects are in effect a (linear) model of your (non-linear) probit model. As all models it is not an exact representation of what it summarizes. This does not have to be a problem as long as it is a useful simplification. However, with interaction effect this "friction" becomes so large that it is no longer useful. Basically, you'll end up with a "conclusion" that for some individuals the interaction effect is significantly positive, for other it is significantly negative, and for the remaining individuals it is non-significant. What is worse, this variability does not represent an aspect of the data, but instead is the result of the friction between the linear model implied by marginal effects and the non-linear model implied by -probit-. For that reason I prefer the -logit- model and the interpretation in terms of odds ratios. You need to put a bit of effort into helping your audience understand these coefficients, but that is not as hard as many seem to fear. See for example: M.L. Buis (2010) "Stata tip 87: Interpretation of interactions in non-linear models", The Stata Journal, 10(2), pp. 305-308. Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Testing independence of factor variables in a non-linear specification***From:*Tanuku AP <tanuku.ap@hotmail.com>

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